Global existence for the nonlinear equations of crystal optics
Journées équations aux dérivées partielles (1989), article no. 5, 11 p.
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     author = {Liess, Otto},
     title = {Global existence for the nonlinear equations of crystal optics},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {5},
     pages = {1--11},
     publisher = {Ecole polytechnique},
     year = {1989},
     zbl = {0688.35091},
     mrnumber = {1030820},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1989____A5_0/}
}
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Liess, Otto. Global existence for the nonlinear equations of crystal optics. Journées équations aux dérivées partielles (1989), article  no. 5, 11 p. http://www.numdam.org/item/JEDP_1989____A5_0/

J.M. Bony [1] : Calcul symbolic et propagation des singularités pour les équations aux derivées partielles non linéaires. Ann. Sc. E.N.S. 14 (1981), 209-246. | Numdam | MR | Zbl

M. Born - E. Wolf [1] : Principles of optics, 3rd ed., Pergamon Press, 1964.

R. Courant - D. Hilbert [1] : Methoden der mathematischen Physik. vol. II, Springer Verlag, 1937, and revised English version in Interscience Publ., 1962. | JFM | Zbl

F. John [1] : Delayed singularity formation in solutions of nonllinear wave equations in higher dimension. Comm. Pure Appl. Math., 29 (1976), 649-681. | MR | Zbl

F. John [2] : Lower bounds for the life span of solutions of nonlinear wave equations in three dimensions. Comm. Pure Appl. Math., 36 (1983), 1-35. | MR | Zbl

F. John [3] : Almost global existence of elastic waves of finite amplitude arising from small initial disturbances. Comm. Pure Appl. Math., 41:3 (1988), 615-667. | MR | Zbl

T. Kato [1] : The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rat. Mech. Anal. 58 (1975), 181-205. | MR | Zbl

S. Klainerman [1] : Global existence for nonlinear wave equations. Comm. Pure Appl. Math. 33 (1980), 43-101. | MR | Zbl

S. Klainerman [2] : Long time behaviour of solutions to nonlinear wave equations. Proc. Int. Congress Math. at Warsaw 1983. 1209-1215. | MR | Zbl

S. Klainerman-G. Ponce [1] : Global small amplitude solutions to nonlinear evolution equations. Comm. Pure Appl. Math., 36, (1983), 133-141. | MR | Zbl

O. Liess [1] : Decay estimates for solutions of the system of crystal optics. To appear. | Zbl

I.E. Segal [1] : Dispersion for nonlinear relativistic equations. Ann. E.N.S., 4e serie (1968), 459-497. | Numdam | MR | Zbl

I.E. Segal [2] : Space time decay for solutions of wave equations. Advances in Math., 22 (1976), 305-311. | MR | Zbl

J. Shatah [1] : Global existence of small solutions to nonlinear evolution equations. J. diff. equations, 46 (1982), 409-425. | MR | Zbl

A. Sommerfeld [1] : Vorlesungen über theoretische Physik, Bd. III u. IV, Akademische Verlagsgesellschaft, Leipzig, 1964.

W. Strauss [1]: Decay and asymptotics for □u = F(u). J. Funct. Anal. 2 (1968), 409-457. | MR | Zbl

W. Strauss [2] : Everywhere defined wave equations. in “Nonlinear evolution equations”, M.G. Crandall Ed., Academic Press, 1978, 85-102. | MR | Zbl

R.S. Strichartz [1] : Convolution with kernels having singularities on a sphere. Trans. A.M.S., 148 (1970), 461-471. | MR | Zbl

R.S. Strichartz [2] : A priori estimates for the wave equation and some applications. J. Funct. Analysis, 5 (1970), 218-235. | MR | Zbl

M.E. Taylor [1] : Pseudodifferential operators. Princeton University Press, Princeton, New Jersey, 1981. | MR | Zbl

W.V. Wahl [1] : Lp-decay rates for homogeneous wave equations. Math. Zeitschrift, 120 (1971), 93-106. | Zbl

A. Yariv [1] : Quantum electronics, second edition. John Wiley, Sons, Inc., New York - London - Sydney - Toronto, 1975.